TO PREPARE THE TARRAGON BUTTER: Saute the shallots in 1 teaspoon butter for 3-4 minutes, or until beginning to brown. Stir into the remaining butter, along with the tarragon. Divide into two mounds; flatten between sheets of wax paper. Place in the freezer.

TO COOK THE STEAKS: Preheat the oven to 400 degrees F. Heat the oil in a cast-iron skillet or oven-proof pan over high heat. salt and pepper the filets. Brown on all sides. Put the pan in the oven; bake for 5 minutes (for medium-rare). Let the steaks rest several hours before serving. When ready to serve, top with Tarragon Butter.